an introduction to catastrophe insurance … · an introduction to catastrophe insurance futures...

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AN INTRODUCTION TO CATASTROPHE INSURANCE FUTURES Michael Bayard Smith L. Jaimie Pickles Consulting Actuary Financial Consultant Tillinghast, A Towers Perrin Company Tillinghast, A Towers Perrin Company 1200 Gulf Life Drive, Suite 610 200 West Madison Street, Suite 3400 Jacksonville, Florida 32207 Chicago, Illinois 60606 Telephone: 904-398-5661 Telephone: 312-609-9400 Telefax: 904-399-8267 Telefax: 312-609-9393 The goal of the paper is to introduce catastrophe insurance futures and options. We first provide background on natural catastrophes and the associated financial effects on both the primary and reinsurance markets for property insurance. Next, we describe the recently introduced catastrophe insurance futures product and present a general framework for its pricing. We then illustrate the risk management and speculation potential of the futures contracts with several examples. In conclusion, we discuss the future of the contract and suggest several areas for further research. 817

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Page 1: AN INTRODUCTION TO CATASTROPHE INSURANCE … · AN INTRODUCTION TO CATASTROPHE INSURANCE FUTURES ... both the primary and reinsurance markets for property ... Insurance companies

AN INTRODUCTION TO CATASTROPHE INSURANCE FUTURES

Michael Bayard Smith L. Jaimie Pickles Consulting Actuary Financial Consultant

Tillinghast, A Towers Perrin Company Tillinghast, A Towers Perrin Company 1200 Gulf Life Drive, Suite 610 200 West Madison Street, Suite 3400

Jacksonville, Florida 32207 Chicago, Illinois 60606 Telephone: 904-398-5661 Telephone: 312-609-9400

Telefax: 904-399-8267 Telefax: 312-609-9393

The goal of the paper is to introduce catastrophe insurance futures and options. We

first provide background on natural catastrophes and the associated financial effects on

both the primary and reinsurance markets for property insurance. Next, we describe the

recently introduced catastrophe insurance futures product and present a general framework

for its pricing. We then illustrate the risk management and speculation potential of the

futures contracts with several examples. In conclusion, we discuss the future of the

contract and suggest several areas for further research.

817

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introduction aux contrats 31 terme sur assurance des risques de catastrophe

Michael Bayard Smith L. Jaime Pickles Actuaire Conseil Conseiller financier Tillinhast, A Towers Perrin Company Tillinhast, A Towers Perrin Company 1200 Gulf Life Drive, Suite 610 200 West Madison Street, Suite 3400 Jacksonville, Florida 32207 Chicago, Illinois 60606 Telephone : 904-398-5661 Telephone : 312-609-9400 Fax : 904-399-8267 Fax : 312-609-9393

Msum6

Le but du present expose est d’introduire les options et contrats 3 terme sur

l’assurance des risques de catastrophe Nous presentons tout d’abord des donnees

g&r&ales sur les catastrophes naturelles et leur impact financier a la fois sur les

marches primaires et sur les marches de reassurance de la propriete. Nous decrivons

ensuite le produit recemment introduit de contrats a terme sur assurance des risques

de catastrophe et presentons un cadre general permettant d’btablir son prix. Nous

illustrons ensuite la gestion du risque et le potentiel de speculation des contrats &

terme ZI I’aide de quelques exemples. En conclusion, nous traitons de I’avenir du

contrat et suggerons plusieurs secteurs pouvant faire I’objet de recherches

supplementaires.

818

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AN INTRODUCTION TO CATASTROPHE INSURANCE FUTURES 819

INTRODUCTION

Natural catastrophes place significant financial demands on society. In recent years the

magnitude of catastrophe losses (both insured and uninsured) has been staggering.

Insurance markets are faced with the dilemma of increasing consumer demand and

decreasing reinsurance supply. Partly in response to and partly in anticipation of current

insurance (and reinsurance) market conditions, financial markets have responded.

Derivative financial instruments linked to the level of catastrophe losses have been

introduced in the United States and are under consideration in Europe. To date market

activity has been thin (in the sense of few players and minimal volume) with the notable

exception of call option spreads on the futures contract.

In the sections that follow more background is given on natural catastrophes and the

insurance/reinsurance markets (in particular current market conditions for property

insurance and property catastrophe reinsurance.) Then, the catastrophe insurance futures

product is described, and pricing considerations are set forth relative to the empirical

evidence from the market. A general pricing structure is introduced. Several illustrative

examples of hedging applications are presented. In conclusion, the future of catastrophe

insurance futures is discussed.

NATURAL CATASTROPHES AND INSURANCE/REINSURANCE MARKETS

Natural catastrophes cause significant loss to life and damage to property. Large

international reinsurers and others devote significant resources to the analysis of such

catastrophes (Munich Reinsurance, 1988; Swiss Reinsurance, 1993).

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Although natural catastrophes are at least as devastating outside the United States, for

the current purpose, we will concentrate on natural catastrophes within the United States.

Appendix Exhibit 1 shows quarterly catastrophe loss ratios defined as quarterly catastrophe

losses estimated by Property Claim Services (PCS), a subsidiary of the American Insurance

Association, divided by quarterly earned premium from AM Best Company. Particularly

noteworthy are the loss ratios for the third quarters of 1989 and 1992 which include the

catastrophe losses arising from Hurricanes Hugo and Andrew, respectively.

The following chart shows the statistics arising from the quarterly PCS/AM Best

catastrophe loss ratios:

CATASTROPHE LOSS RATIO STATISTICS, -1992

FIRST QTR

SECOND QTR

THIRD QTR

FOURTH QTR

Ranqe

0.39% - 6.62%

0.40% - 27.57%

0.23% - 103.17%

0.09% - 8.47%

Mean

1.82%

5.35%

7.72%

2.14%

Std. Deviation

1.43%

5.34%

20.72%

2.47%

The previously mentioned Hurricanes Hugo and Andrew contribute to the loss quarter

of their occurrence being at the 99th and 100th percentile for the historical period studied.

The uncertainty associated with catastrophes plus recent record loss levels have

required enormous economic and social resources. Property owners have dealt with

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AN INTRODUCTION TO CATASTROPHE INSURANCE FUTURES 821

physical injury and death in addition to loss of property. Insurance company resources and

government aid programs have been stressed responding to financial claims for disaster

relief. Reinsurers stand behind the insurance companies providing financial resources, and

taxpayers ultimately fund government relief programs.

Property owners, especially in catastrophe prone areas, are faced with the unavailability

of insurance coverage as well as an increased deductible level, restricted coverage and

increased prices when coverage is available. Insurance companies are faced with increased

demand from insureds, regulatory restrictions on price increases, and increasing retention

levels and prices associated with decreasing reinsurance capacity. Reinsurers, once able to

retrocede risk to other reinsurers, are now accepting business from ceding companies with

extremely limited retrocession support (Schnieper, 1993). Governments, as regulators of

the insurance markets, play a role administering the estates of companies rendered

insolvent by catastrophes, and organizing governmental or quasi-governmental facilities

providing primary insurance or reinsurance capacity. Governments are also involved in

financing risk handling facilities, providing disaster relief assistance directly and through

government loans.

Financial institutions, particularly those with large mortgage portfolios, are recognizing

the risks and examining mechanisms for managing the risk. The same risk management

approach would apply to large property owners.

There are clear signals of a crisis with financial and social implications. In the spirit of

innovation, the Chicago Board of Trade (CBOT) launched catastrophe insurance futures and

options in late 1992. The financial market features of market price discovery and the

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potential for additional liquidity provide an interesting alternative to consider for mitigating

the crisis.

The next section describes the catastrophe insurance futures and options.

CATASTROPHE INSURANCE FUTURES b OPTIONS

Although insurance futures and options have been considered for many years prior to

1992, the CBOT has been the first organization to devote the developmental resources to

bring such products to market. After consideration of health insurance and automobile

physical damage insurance futures contracts, the CBOT introduced catastrophe insurance

futures and options on futures in December 1992.

The futures contracts settlement price was based on an index calculated by dividing

quarterly “catastrophe” losses incurred in a given loss quarter and reported during that

quarter or the next quarter by earned premium based on overall historical market statistics.

The “catastrophe” losses were defined as losses for a particular line of business and cause

of loss from data reported to ISODATA, Inc. (ISODATA), an insurance industry statistical

organization, by a group of 22 insurance companies. The reported catastrophe losses are

adjusted to total market levels based on the relationship of reporting company premiums to

market premiums. The plan was to introduce National, Eastern, Midwestern and Western

contracts. National and Eastern contracts were released in December 1992; the Midwestern

in May 1993.

In an effort to educate the marketplace, the CBOT released historical “simulations” of

final settlement prices based on reconstruction of loss data reported to ISODATA and the

current premium base for the initial contracts. The construction of the historical

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AN INTRODUCTION TO CATASTROPHE INSURANCE FUTURES 823

“simulation” could lead to a slight understatement of the mean settlement value for a loss

quarter and an overstatement of the variability. The historical “simulations” of settlement

prices are presented below:

‘Simulated’ Futures Settlement Prices, 3089 - 3092

(Catastrophe Loss Ratio x $25,000)

2nd National

Eastern

1989

$6,375

$12,075

$1,800

$1,425

$1,175

$2.325

$1,525

$2,800

$825

1991 I 1992 I Mean Standard

1 1 1 Deviation

$1,950 $2,225 $1,867 $406

$1,375 $4,100 $2,217 $1,634

$4,225 $4,325 $3,625 $1,127

$2,750 $1,925 $2,067 $625

$1.475 $24,800 $9,692 $13,100

51.875 $44.725 $15,808 $25,048

$775 - $1,108 $599

$650 - $1,017 $437

Actual settlements have been effected for the fourth loss quarter of 1992 and the 1st

loss quarter of 1993.

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824 4TH AFIR INTERNATIONAL COLLOQUIUM

Actual Futures Settlement Prices, 4092 - 1093

(Catastrophe Loss Ratio x $25,000)

Loss Quarter Region 1992 l 1993 l A Priori Statistics l *

Mean

4th National $2,000 -

Eastern $3,575 -

1st National - $3,825

Eastern - $6,125

l From CBOT Settlement Reports

$1,108

$1,017

$1,867

$2,217

A Priori Statistics l *

Standard Deviation

$599

$437

$406

$1,634

l * Based on ISODATA historical simulations

From the results above, the historical simulations (which are quite limited) did not

provide reliable predictive value for the first two actual settlements. However, the two

actual settlements do provide further evidence of the uncertain and skewed nature of the

distributions underlying the “catastrophe losses” first indicated by the statistics for the third

quarter settlement prices.

PCS loss data combined with AM Best premium have also been used to illustrate

historical catastrophe loss ratios (CBOT, 1993). Although of potential value in analyzing the

pricing, there are several differences between the two data sets that would require careful

consideration as part of any detailed analysis.

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AN INTRODUCTION TO CATASTROPHE INSURANCE FUTURES 825

CATASTROPHIC LOSS PROCESS

Since the futures contracts are restricted to a given loss quarter, the flow of information

about catastrophes within the loss quarter will likely have considerable effect on price

discovery within the marketplace. An idealized graphical description of the loss process

and the reporting process is shown below:

The incurred losses, although idealized, begin at zero at the beginning of the loss

quarter and reach the maximum value at the end of the loss quarter. The reported losses

lag the incurred losses and reach the ultimate incurred value many months after the actual

settlement has taken place for a particular loss quarter. Tools for detailed analysis of the

loss development process are part of the typical education of a casualty actuary in the

United States. The limited time horizon and the risk of a significant catastrophe make such

analysis difficult in actual applications.

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826 4TH AFIR INTERNATIONAL COLLOQUIUM

Data quality issues and real time processing practicalities necessitate that the interim

reported value (as of the end of the loss quarter) is only publicly announced at the end of

the reporting period, and the final settlement is only publicly announced approximately

three months after the end of the reporting period.

Various loss distributions can be considered for modeling the catastrophe loss

distribution. Investigators have applied frequency/severity compound distributions to study

United States hurricanes (Levi b Partrat, 1991) Direct modeling of the compound aggregate

distribution is also a possibility.

The “catastrophic” losses included in the CBOT contract will include hurricanes,

earthquakes, and other catastrophes as well as a core of non-catastrophic losses

conforming to the cause of loss/line of business data definitions. Thus, any “catastrophic”

loss model by component should include a basic variable of limited variability plus variables

of greater variability corresponding to each significant type of natural catastrophe.

Other useful tools for analyzing the catastrophe losses are the various exposure/damage

models. These models rely on distributed exposure data and simulate the effects of

windstorms, earthquakes, tornados, and other natural catastrophes. The output of the

model simulation exercise could then be used to construct an aggregate loss distribution for

the catastrophic components of the futures contract. Coupled with the basic component

described above, the total “catastrophe” aggregate loss distribution could be used to

estimate futures settlement prices (and confidence intervals) and to investigate the behavior

of options on the catastrophe insurance futures.

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AN INTRODUCTION TO CATASTROPHE INSURANCE FUTURES 827

Within a given loss quarter, the level of incurred “catastrophic” losses is monotonically

increasing and is dramatically affected by the occurrence or non-occurrence of major

catastrophes. Accordingly models for the process need to take account of the informational

value of actual catastrophes in the loss quarter relative to expected catastrophes estimated

prior to the loss quarter.

EMPIRICAL MARKET OBSERVATIONS

As mentioned previously, the trading to date for futures has been very limited. Starting

in July 1993, there has been some trading of options on the futures contract in the form of

call option spreads synthesizing a layer of catastrophic reinsurance. Such trading activity

has been concentrated in the loss quarters ending September 1993 and December 1993.

From inception to settlement the future contracts that have exhibited the following price

ranges:

Loss Quarter

4th Quarter 1992

1st Quarter 1993

Region Price Range Final Price

National $2,000 - $3,000 $2,000

Eastern $2,175 - $4,850 $3,575

National $2,025 - $4,000 $3,825

Eastern $1,750 - $8,775 $6,125

The daily prices for these contracts as well as volume are shown in Appendix Exhibit 2,

Sheets 1 - 6.

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828 4TH AFIR INTERNATIONAL COLLOQUIUM

POTENTIAL USES OF CATASTROPHE INSURANCE FUTURES AND OPTIONS ON FUTURES

Hedqina with Futures

An insurer with significant exposures on the East coast is interested in protecting itself

from unexpected catastrophic losses. The insurer can construct synthetic catastrophe

reinsurance by purchasing September 1994 Eastern futures contracts. These contracts

cover losses occurring on the East coast in the third quarter. The insurer and the industry

have the following expectations:

3rd Quarter 1994 Insurer

Incurred Losses $2 million

Earned Premiums $5 million

Industry

$2.4 billion

$6.0 billion

The insurer assumes that its losses are perfectly correlated with the industry’s. Further,

it is expected that 75% of the industry’s ultimate third-quarter losses will be reported to IS0

DATA by December 31, 1994. With this information, the rational opening price of the

September 1994 Eastern futures will be $7,500 [$25,000 x (($2.4 billion x 75%)/$6 billion)].

The insurer should purchase 267 contracts [$5 million/($25,000 x 75%)] to create a

hedge against larger than expected losses. The CBOT requires a margin to be deposited;

however, this margin price is substantially less than the $7,500 contract price.

The table below illustrates that the insurer establishes a hedge by “locking in” an

expected loss ratio.

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AN INTRODUCTION TO CATASTROPHE INSURANCE FUTURES 829

Loss Ratio

Futures Price

Original Futures Price

Net Futures Gain (Loss)

Number of Contracts

Gain (Loss) on Futures ($1.001.250) 0 $1.001.250 $2,002,500 $3.003.750

Unexpected Gain (Loss)

on Insurer’s Book of

Business

Net Position ($1,250) 0 $1,250

$7,500

($3.750)

267

$1.000.000

267

0

60%

$11,250

$7,500

$3,750

267

($1.000.000)

267 267

($2.000.000) ($3.000,000)

--&q-G-

Hedoino with Futures and Ootions on Futures

If an insurer wants to hedge against losses up to a specific loss ratio, it could

simultaneously purchase insurance futures and options on futures. The following example

uses the same assumptions in the previous example; however, we will assume that the

company believes its ultimate loss ratio and the ISODATA ultimate loss ratio will not exceed

100%. The company buys 267 Eastern September futures contracts. In addition, the

company sells 267 Eastern September call option contracts with a 100% loss ratio strike

(X= 100).

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The hedge is effective up to a 100% loss ratio, and the company profits from selling the

option (267 x option premium). However, if the loss ratio exceeds a 100% loss ratio, the

company experiences a negative net position.

Hedoino with Ootions on Futures

Consider again the insurer we used in the above “Hedging with Futures” example. If a

company’s objective is to protect itself against a loss ratio greater than 40%, it would

similarly purchase 267 September 1994 Eastern call options with a strike price of 40 (i.e.,

40% loss ratio). The table below illustrates the results of this hedge.

Loss Ratio

Futures Price

Gain per Options

contract

Number of

Contracts

Gain on Options

(before Option

Premium)

0 0 $1,001,250 $2,002,500 $3,003,750

Unexpected Gain $1 ,ooo,ooo 0 ($1,000,000) ($2,000,000) ($3,000,000)

(Loss) on Insurer’s

Book of Business

Net Position $1,000,000 0 $1,250 $2,500 $3,750

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AN INTRODUCTION TO CATASTROPHE INSURANCE FUTURES 831

Recent Market Develooments

After the CBOT repositioned its insurance derivative products in July 1993, companies

have been using call option spreads to hedge “layers” of insurance losses. Instead of

purchasing traditional forms of reinsurance, a company could hedge its exposures above a

specific amount of retained losses up to a maximum level of losses. The CBOT has referred

to this strategy as constructing “synthetic reinsurance.”

To create synthetic reinsurance, a company could establish the following position:

l Buy Eastern September 1994 call options with a strike of 60

Each call has a price of 20 ($5,000)

a Sell Eastern September 1994 call options with a strike of 100

Each call has a price of 15 ($3,750)

This position creates an initial net debit position of 5 ($1,250); therefore, the company’s

exposures are hedged against losses once the ISODATA loss ratio exceeds 65%. Coverage

exists up to a 100% loss ratio. This assumes perfect correlation between the company’s

losses and the losses of the companies reporting to ISODATA. A detailed analysis should

be conducted by individual companies to determine the strike prices that will hedge layers

of exposure (e.g., $50 million excess of $50 million).

Soeculatina with Options on Futures

Individual speculators can also use call options spreads similar to the above example.

They would simply take the opposite position by selling the call with a low strike and

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832 4TH AFIR INTERNATIONAL COLLOQUIUM

purchasing a call with a higher strike. Each point between the spread is worth $250;

therefore, the 60/100 spread would create a $10,000 exposure.

Similarly, a reinsurer could sell layers of insurance by selling a call spread. In fact, some

argue that catastrophe insurance options on futures provide effective diversification more

efficiently than utilizing traditional reinsurance distribution channels (CBOT, 1993).

Arbitraqe Oooonunities

Given the nature of this product and the fundamental lack of market information, it is

difficult to develop an accurate pricing model. Individuals and companies that can construct

pricing models may be able to make arbitrage profits.

When the market matures and liquidity is sufficient in trading futures and options on

futures (calls and puts), arbitrage profits will exist if the American put/call parity does not

hold. The American put/call parity applies if the following relationship exists:

C - FO,T + (e”-f?A)K =z= P c= C - (e^-RA)FO,T + K

Where:C = Price of call

FO,T = Spot price of futures contract

(e^-RA)K = Present value of strike price

P = Price of put

(e A -RA)FO,T = Present value of futures spot price delivered at futures maturity

date (Time = A)

K = Strike price

The following table illustrates the conditions that must be met in order to avoid arbitrage

opportunities:

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AN INTRODUCTION TO CATASTROPHE INSURANCE FUTURES 833

Action

Buy Call

Sell Put

Sell Futures

Borrow

;Risk Free Rate)

Column Totds

Inflow at Time Zero Inflow at Time = A

FA,T <= K

-C 0

,-G-/-s (e”-RA)(FO,T - K) -FO,T + K

Must equal zero 0

Inflow at Time = A

FA.T > K

FA,T - K

0

-(FA,T - F0.T)

-FO,T + K

0

By simultaneously selling the put, selling the futures contract and borrowing at the risk

free rate, a short position in a “synthetic” call is created. Therefore, if the true call price

does not equal the synthetic call price, an opportunity to make arbitrage profits exists. For

example, if the call is underpriced, the position created in the table above would produce an

arbitrage profit at “Time Zero.” If the call is overpriced, reverse the positions (i.e., sell the

call, buy the put, buy the futures contract and lend at the risk free rate).

THE FUTURE OF INSURANCE DERIVATIVES

Currently, this alternative market is providing only several million dollars of synthetic

reinsurance capacity. In October 1993, the CBOT estimated this number to be

approximately $6 million dollars. When this paper is presented, these insurance derivatives

will have been traded for over one year. However, it is difficult to predict if the insurance

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834 4TH AFIR INTERNATIONAL COLLOQUIUM

industry will incorporate the contracts into their fundamental risk management strategies, as

a number of barriers to success remain:

Financial Innovation - The learning curve remains steep, and many individuals and

companies are reluctant to incorporate hedging activity into their business strategy.

Requlation - The National Association of Insurance Commissioners (NAIC) has not yet

determined specific accounting practices and procedures for insurance derivatives. This

announcement is expected in 1994. In the U.S., regulations have been implemented in

Illinois and are expected to take effect in New York and California in 1994.

Liauiditv - Traders face significant liquidity problems, as volume remains low in this

market.

Participants - lt is difficult to identify natural sellers in this market. However, reinsurers,

Wall Street and institutional investors have expressed an interest in these products and

may emerge as sellers.

Pricing - Given the nature of this product and the lack of information available to buyers

and sellers, it is difficult to determine prices of the contract. Until an accurate pricing

model is created, market trading volume will remain low.

It is necessary to conduct further research to develop accurate pricing models. For

example, premiums, by state and line of business, would be converted to exposure values.

Subsequently, exposure values would be geographically distributed. Once this is

accomplished, the model would, based on fundamental assumptions, simulate the effects of

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AN INTRODUCTION TO CATASTROPHE INSURANCE FUTURES 835

catastrophic events (hurricane, tornado, earthquake, hail, etc.). These statistics could then

be used to estimate expected prices for futures and options on futures. Further, during the

loss period of contracts, participants could use models to estimate the impact of

catastrophes, before and after the events.

Other pricing models could be based on’historical information. As the market develops,

PCS and ISODATA statistics may be used to estimate expected prices. There appear to be

many areas of fruitful research open to those interested in this innovative new product.

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836 4TH AFIR INTERNATIONAL COLLOQUIUM

APPENDIX

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Irn4b

20%

Exhibit 1 National Catastrophe Loss Ratio

1 r

Source: PCS/AM But Year

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838 4TH AFIR INTERNATIONAL COLLOQUIUM

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EXHIBIT 2 Sheet 2

Chicago Board of Trade Eastern Catastrophe Insurance Futures Daily Volume

90

80

70

60

02 50 !? 2 40

30

20

10

0 ll-Dee 26-Jan lo-Mar 22-Apr 04-Jun 19-Jul 30-Aug

Trading Date

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840 4TH AFIR INTERNATIONAL COLLOQUIUM

I

I I

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EXHIBIT 2 Sheet 4

20

15

.z 10 &

5

0 11-Dee

Chicago Board of Trade National Catastrophe Insurance Futures Daily Closing Prices

n 15.3

J-

26-Jan lo-Mar 22-Apr 04-Jun 19-Jul 30-Aug Trading Date

__ March (formerly June)

- - Settle Price

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842 4TH AFIR INTERNATIONAL COLLOQUIUM

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EXHIBIT 2 Sheet 6

30

25

20

.B 15 2

10

5

0

-

Chicago Board of Trade Eastern Catastrophe Insurance Futures Daily Closing Prices

ll-Dee 2h- Jan lo-Mar 22-Apr 04-Jun 19-Jul M--Au&

Trading Date

__ March (formerly June)

- - Settle Price

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844 4TH AFIR INTERNATIONAL COLLOQUIUM

REFERENCES

1 Chicago Board of Trade (1992) Reference Guide: Catastrophe Insurance Futures and

Options. CBOT, Chicago.

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